
Brant Jones
Department of Mathematics and Statistics

Since joining JMU, I've mentored several undergraduate research projects for students majoring in math and computer science, both locally as well as part of the NSF REU site that we host during the summer. In 2013, I was invited to participate as a visiting researcher in the semester program on Combinatorial Representation Theory at the Institute for Computational and Experimental Research in Mathematics (ICERM).
My research interests include algorithms, algebraic structures, and enumerative combinatorics, particularly as related to the representation theory of reflection groups.
Teaching I have been awarded a sabbatical semester for Fall 2016. Some of my previous classes include:
Some Papers Especially For or By Undergraduate Researchers
Rational generating series for affine permutation pattern avoidance
The Refined Lecture Hall Theorem via Abacus Diagrams (with Laura Bradford, Meredith Harris, Alex Komarinski, Carly Matson, and Edwin O'Shea)
Solitaire Mancala Games and the Chinese Remainder Theorem (with Laura Taalman and Anthony Tongen)
Permutations, Pattern Avoidance, and the Catalan Triangle (with Derek Desantis, Rebecca Field, Wesley Hough, Rebecca Meissen, and Jacob Ziefle)
Missouri Journal of Mathematical Sciences 25 (1) (2013) 5060 preprint version
Additional Publications (with descriptions)
Results and conjectures on simultaneous core partitions (with Drew Armstrong and Christopher R. H. Hanusa)
Using carrytruncated addition to analyze addrotatexor hash algorithms (with Rebecca Field)
Mask formulas for cograssmannian KazhdanLusztig polynomials (with Alexander Woo)
Abacus models for parabolic quotients of affine Weyl groups (with Christopher R. H. Hanusa)
Affine structures and a tableau model for E_{6} crystals (with Anne Schilling)
The enumeration of maximally clustered permutations (with Hugh Denoncourt)
The enumeration of fully commutative affine permutations (with Christopher R. H. Hanusa)
An explicit derivation of the Möbius function for Bruhat order
A bijection on core partitions and a parabolic quotient of the affine symmetric group (with Chris Berg and Monica Vazirani)
Leading coefficients of KazhdanLusztig polynomials for Deodhar elements
KazhdanLusztig polynomials for maximallyclustered hexagonavoiding permutations
Embedded factor patterns for Deodhar elements in KazhdanLusztig theory (with Sara C. Billey)
Mathematical Software
Sage: I have contributed some code to sage.combinat, particularly an initial implementation of the LenartPostnikov alcove path model for crystals.
liberiksson: A C++ library to perform fast computations on elements of Coxeter groups, used for some of my papers on KazhdanLusztig polynomials. More specifically, the code classifies the Deodhar elements of finite Coxeter groups by embedded factor containment, and verifies that the mu coefficients for KazhdanLusztig polynomials associated to these elements are always 0 or 1.
Erdős number: 3 